polarized raman of nanoscale two-dimensional materials

Polarized Raman of Nanoscale Two-Dimensional Materials:Combined Optical and Structural EffectsHamidreza Zobeiri,†,∥ Ridong Wang,†,∥ Cheng Deng,§ Qianying Zhang,*,‡ and Xinwei Wang*,†

†Department of Mechanical Engineering, Iowa State University, Ames, Iowa 50011, United States‡College of Metallurgy and Material Engineering, Chongqing University of Science & Technology, University Town, HuxiShapingba District, Chongqing 401331, P. R. China§College of Mechatronics Engineering, Guangdong Polytechnic Normal University, Guangzhou 510635, People’s Republic of China

ABSTRACT: The intensity response of polarized Raman isstudied using backscattered Raman spectroscopy. In previousworks, it was confirmed that the Raman intensities of the E2g

1

modes for WS2 and MoS2 as well as the G mode of grapheneare independent of the polarization angle. However, a strongcorrelation is found between them in this work using aconfocal Raman system. The E2g

1 and A1g modes ofnanometer-thick WS2 and MoS2 samples as well as the Gmode of bulk graphene are used to investigate the polarizationdependency of the Raman intensity for each mode. Addition-ally, the effects of temperature and sample structure on theRaman intensity are studied using the WS2 sample on bothsuspended and supported areas. Results of these experiments are explained and fitted by the theoretical Raman intensity profiles.This theoretical study is conducted using the classical theory of polarized Raman spectroscopy and includes all the informationabout polarization of excitation laser, rotation of the beam splitter, and different vibrational modes of samples, which isconsidered in Raman tensors. It is concluded that Raman intensity variation with incident laser polarization not only is afunction of the material structure but also carries information about the optical functionality of the Raman system.

1. INTRODUCTION

Raman spectroscopy is becoming a powerful tool to character-ize the thermal, charge carrier, and structural properties ofmaterials. Raman spectroscopy can provide information aboutthe electronic structures,1,2 lattice vibration and crystallo-graphic orientations,3−7 hot carrier and thermal transport,8−10

and charge transfer of these materials.11,12 One of thetechniques that probe information about the crystal orientationand symmetry of bond vibrations is polarized Ramanspectroscopy. It is a promising technique for polarizationmeasurement since the lasers used for excitation are naturallylinearly polarized.Polarized Raman spectroscopy could be conducted using

different typical setups based on polarization of incident orscattered light or rotation of the sample. In one configuration,only the incident laser light is polarized while the analyzer isheld constant, and scattered light is not polarization-controlledbefore entering the spectrometer.13,14 In another configuration,polarization of incident light is either vertical or horizontal,while the polarization of the scattered light is tuned by ananalyzer.3,15,16 It is possible to combine the last twoconfigurations and control the polarization of the incidentand scattered lights simultaneously. If the polarizer is insertedin the path of incident and scattered laser lights, they will beboth polarized in a similar direction. By using two polarizers, itis possible to polarize both lights in separate directions.17,18

While the aforementioned setups are adjusted by the positionof the polarizer, another possible configuration could berotating the sample around the laser beam, while thepolarization of incident and scattered lights is constant.19,20

Polarization measurements could be used to identify thecrystal orientations of several ordered materials. Wang et al.developed the optothermal Raman spectroscopy (OT-Raman)method to identify the crystalline orientation of blackphosphorus (BP).14 They could identify the crystallineorientation of BP regardless of sample thickness and excitationwavelength using Raman frequency-power differential Φ = ∂ω/∂P. Φ is minimum (maximum) when laser polarization is alongthe zigzag (armchair) direction. Duesberg et al. performedpolarized micro-Raman spectroscopy on spatially separatedsingle-wall CNTs, and it revealed that, when nanotubes arealigned parallel to the polarization of the incident light, theintensities of all Raman modes are maximum.21 Zhang et al.determined the crystalline orientation of phosphorene flakeswithout tunneling electron microscopy by polarized Ramanspectroscopy.22 Wang et al. used polarized micro-Ramanspectroscopy to study the crystallographic orientation ofmonolayer MoS2 under controllable uniaxial tensile strain.3

Received: July 19, 2019Revised: August 23, 2019Published: August 28, 2019

Article

pubs.acs.org/JPCCCite This: J. Phys. Chem. C 2019, 123, 23236−23245

© 2019 American Chemical Society 23236 DOI: 10.1021/acs.jpcc.9b06892J. Phys. Chem. C 2019, 123, 23236−23245

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They showed that the doubly degenerate E2g1 mode splits into

two modes, namely, E2g1+ and E2g

1−. The intensities of thesesubmodes respond to the angle between the strain axis andpolarization of the scattered light, orthogonally. Ribeiro et al.studied the angular dependence of polarized Raman spectra forthe Ag

1, Ag2, and B2g modes in both parallel and cross-

polarization configurations using three different lasers withthree wavelengths and concluded that Raman tensors exhibitcomplex elements.23 They measured the phase differencebetween each laser line and Raman tensor elements for eachmode and observed that phase differences are much smaller forthe out-of-plane Ag

1 mode than for the in-plane totallysymmetric Ag

2 mode.In this work, we study the intensity response of polarized

Raman using a confocal Raman system. Both E2g1 and A1g

Raman modes of WS2 and MoS2 and G mode of graphenepaper are used to analyze the responses of Raman and opticalsystems. Also, this analysis is conducted at different temper-atures for the WS2 sample on both suspended and supportedareas. It is discovered that the final Raman intensity variationwith excitation laser polarization cannot be simply interpretedas the structural effect, but rather it includes information aboutthe optical system.

2. EXPERIMENTAL SECTIONFigure 1a1 shows the polarized Raman configuration used inthis work. The measurements are conducted at roomtemperature or other temperatures using a BWTEK Voyageconfocal Raman system. Raman spectra are excited using acontinuous wave (CW) laser with 532 nm wavelength(Excelsior-532-150-CDRH, Spectra-Physics) and collected inthe backscattering configuration. A neutral density (ND) filteris used to adjust the laser power, and a half-wave plate is

applied to adjust the polarization of the incident beam. Afterpassing the ND filter and polarizer, the laser beam goesthrough the beam splitter and part of that is reflected andfocused on the sample using a 20× objective lens. Thetemperature of the sample is controlled by an optical cellchamber. The chamber is filled by N2 gas and rapid inlet andoutlet of N2 to control the temperature. This chamber is notshown in Figure 1. More information about it can be found inour previous work.24 The rest of the laser beam is transmittedthrough the beam splitter, which is shown using the dottedline. The scattered Raman signal from the sample transmitsthrough the beam splitter and after passing the notch filter isfocused using a second objective lens onto the slit of thespectrometer. A notch filter is used to block the reflected laserbeam. Then the Raman signal is directed onto the diffractiongrating using a mirror. The grating disperses the spectralcomponents of the Raman light at slightly varying angles,which determines the optical resolution and wavelength rangethat the spectrometer achieves, as shown in Figure 1a2. Finally,the dispersed light is focused by another mirror and imagedonto the CCD detector (Figure 1a3). More details about ourRaman system and its components can be found in ourprevious works.8,25 Figure 1c shows the Raman spectra of WS2,MoS2, and graphene paper. In this work, we use the E2g

1 andA1g peaks of MoS2 and WS2 and the G peak of graphene paperto perform our analysis.

3. RESULTS AND PHYSICS3.1. Polarized Raman of WS2: Experimental Observa-

tion. Few-layered WS2, MoS2, and graphene paper samples areprepared by the mechanical exfoliation and transfer method.Mechanical exfoliation is one of the most successful techniquesto obtain few-layered nanocrystals with high quality from bulk

Figure 1. (a1) Schematic of polarized Raman system. The suspended or supported sample is irradiated by the 532 nm CW laser. Laser power andpolarization of the incident beam are controlled by the ND filter and polarizer, respectively. (a2) Diffraction grating splits and diffracts laser light indifferent wavelengths. (a3) Different components inside the spectrometer. The laser beam is diffracted by grating and reflected onto the CCDsensor by the concave mirror (mirror 2). The CCD detector converts the photons to electrons, which are digitized to a computer. (a4) Preparedsuspended WS2 sample by mechanical exfoliation technique. MoS2 and graphene paper samples are transferred similar to the bare Si substrate. (b)Definition of the incident polarization angle (β) and angle of rotation of beam splitter about the z axis (α). s- and p-polarized directions are paralleland normal to the direction of the beam splitter, which is shown by the black dashed line. Here, the x−y coordinate is attached to the samplestructure. (c) Raman spectra of MoS2, WS2, and graphene paper excited by the CW laser. The E2g

1 and A1g Raman modes of WS2 and MoS2 and Gpeak of graphene paper are observed.

The Journal of Physical Chemistry C Article

DOI: 10.1021/acs.jpcc.9b06892J. Phys. Chem. C 2019, 123, 23236−23245

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layered structures. First, a thick layer of material is peeled offfrom the bulk structure using Scotch tape. Then this layer istransferred to a gel film. Exfoliation using the gel film isconducted several times to achieve the desired thickness of thefew-layered sample. After finding the desired area, the sampleis transferred to a silicon substrate with a hole in it. The holediameter is 10 μm, and its depth is 3 μm. A side view of thissample is shown in Figure 1a4, showing both suspended andsupported areas. Only the WS2 sample is transferred to thesubstrate with the hole to investigate the effects of thesubstrate on the polarized Raman intensity and the area nearthe hole used as the supported area. Only the supported area isused for two other materials.Figure 2 shows the AFM images of WS2 and MoS2 samples.

To perform the AFM measurement, we use the supported areaof each sample to avoid damaging the suspended area. Thethicknesses of WS2 and MoS2 samples are 22 and 55 nm,respectively. As shown in Figure 2a3,b3, the roughness profileof each sample is measured as the biggest thickness variation(Δlmax) along a line on the sample surface. Δlmax is larger forthe WS2 sample, which may be due to wrinkles on it. In thiswork, we used bulk graphene paper to perform the Ramanexperiment; therefore, AFM measurement is not conducted forthis sample.

The 532 nm wavelength CW laser that is used in this work isvertically polarized with a polarization ratio of more than100:1. Therefore, if a beam splitter is not rotated about the zaxis, the incident laser that is reflected by beam splitter andirradiates the sample will be polarized along the y-axis direction(as shown in Figure 1b). However, in reality, the beam splitteris rotated about the z axis slightly. Here, this effect isconsidered in detail, and we take the beam splitter rotationangle as α about the z axis (Figure 1b). In fact, α is the anglebetween the projection of the rotated beam splitter onto thex−y plane and the x axis. Based on this configuration,polarization of both incident and scattered lights could beevaluated in both s-polarized (along the beam splitter) and p-polarized (normal to the beam splitter) directions. In Figure1b, ki and ks represent the incident and scattered wave vectors,respectively, and both are along the z direction. Additionally, βindicates the polarization angle of incident light generated bythe polarizer.In some Raman experiments, the photon energy used for

crystal excitation corresponds to a real electronic transition in acrystal. In this case, the scattered Raman intensity will beenhanced. Such a phenomenon is called resonant Ramanscattering. For WS2, the excitonic gap for the B exciton is 2.33eV at room temperature, which is very close to the photonenergy of the 532 nm laser. Excitonic energy increases with

Figure 2. AFM measurement of WS2 and MoS2 samples. (a1,b1) AFM images of two samples. (a2,b2) Thickness profile of each samplecorresponding to the red dashed line in AFM images. (a3,b3) Thickness profiles that indicate the roughness of samples. For both samples,roughness is less than 10% of total thickness.

Figure 3. (a,b) Room-temperature Raman spectra of 22 nm thick WS2 sample on both supported and suspended areas at different polarizationangles, respectively. (c1−c4) Polar plots of Raman intensities of WS2 sample at room temperature. As shown in this figure, the Raman intensities ofboth E2g

1 and A1g peaks reach their minimum when β is around 100 or 280°.



23238


increasing temperature and is far away from the photon energy.Therefore, resonant Raman scattering is expected to happen inour experiment at temperatures close to the room temperature.Again, for the WS2 sample, the energy of excitons is almostresonant to the photon energy of 532 nm laser as thetemperature of the sample is set at ∼330 K.26

As mentioned earlier, the polarized Raman experiment of theWS2 sample is conducted at room temperature as well as othertemperatures using both supported and suspended areas.Figure 3a,b shows seven representative Raman spectra of WS2at room temperature and various polarization angles (β) forboth supported and suspended areas, respectively. Figure 3c1−c4 shows the polar plots of Raman intensities of both modes asβ is varied from 0 to 360°. It is obvious from this figure that

the intensities of both Raman peaks are maximum when β iseither around 15 or 195° and are minimum when β is around100 or 280°. In addition, this experiment is conducted atseveral temperatures to investigate the effect of temperature onthe polarized Raman intensity. These temperatures are selectedin the range of lower and higher than room temperature atwhich resonant Raman occurs. Figure 4 shows the result of thisexperiment. As shown in Figure 4a by the 3D contour map ofWS2 Raman peaks at several temperatures and polarizationangles, as the temperature of supported WS2 increases from270 to 445 K at all polarization angles (β), the Raman intensityof the E2g

1 peak decreases and is maximum at 270 K when the Bexciton energy is equal to the laser photon energy. Note thatlaser power and laser integration time during the experiment

Figure 4. (a,b) 3D contour maps of WS2 Raman peaks for supported and suspended areas, respectively. This contour shows the variation of Ramanintensity against polarization angle in the range of 0 to 180° at different temperatures. Generally, near 350 K, resonant Raman scattering happensand Raman intensity reaches the maximum. (c−f) Polar plots of temperature-dependent polarized Raman intensities of WS2 sample.



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for all above temperatures are held unchanged as 5 mW and 2s, respectively. Meanwhile, for the A1g peak, the resonancetemperature is higher than the E2g

1 peak and is around 410 K.Similar trends are observed using the suspended WS2 sample(Figure 4b). Differences between the resonance temperaturesof the two peaks could be caused by the effect of the 2LA(M)peak on data fitting of the E2g

1 mode. The vibrationalfrequencies of the E2g

1 and 2LA(M) modes are very close,and these two peaks overlap with each other.27 Therefore, it isnot possible to distinguish both peaks exactly using our Ramanspectrometer with a spectral resolution of 1.9 cm−1 atwavenumbers close to the location of the E2g

1 and 2LA(M)peaks. Additionally, comparing Figure 4a,b, we can see that theresonance temperature of the suspended sample is lower thanthat of the supported one. This is caused by a highertemperature rise of the suspended sample under the same laserirradiation. Figure 4c−f represents the same information but inthe form of a polar plot. Again, for both Raman peaks, theintensity is highest at angles near 10 or 190°.3.2. Physics: Combined Structural and Optical

Effects. Contrary to the above observed E2g1 intensity variation

with the polarization angle, in previous works, it has beendocumented that the Raman intensity of the E2g

1 mode isindependent of the polarization angle of the incident light.3,28

However, the beam splitter does not have exactly similarreflectivity and transmissivity in s- and p-polarized directions,and they change with respect to β. Additionally, suchtransmission and reflection change with the light wavelength,which means that transmissivity and reflectivity of the beamsplitter for different Raman peaks could be slightly different. Inthe following, effects of these scenarios on the polarized Ramanintensity are investigated to explain our observed Ramanintensity variation with the polarization angle.Here, we explore the Raman intensity of the scattered light

by considering all of the aforementioned details. Vectors ofincident and scattered photons of both s and p polarizationsare defined below

α

α

α

α

α

α

α

α= = =−

=−

e A e C e B e Dcos( )

sin( )

0

,

cos( )

sin( )

0

,

sin( )

cos( )

0

,

sin( )

cos( )

0is

ss

ip

sp

Ä

Ç

ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ

É

Ö

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

Ä

Ç


É

Ö


Ä

Ç


É

Ö


Ä

Ç


É

Ö

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑÑ(1)

where A and B are factors that are reflectivities of the beamsplitter in the parallel and normal directions (s and ppolarizations) and C and D represent the transmissivities ofthe beam splitter in these two directions, respectively. By doingso, we consider that the beam splitter has different reflection(or transmission) in parallel and normal directions to the beamsplitter.Using the classical theory of the polarized Raman spectrum,

we can understand the polarization dependence of the Ramanintensity as below

∝ | |I e Rest

i2

(2)

where R describes the Raman tensor of each Raman mode andis represented by a 3 × 3 matrix and es

t is the transpose of the escolumn vector as defined in eq 1. Using eq 2, the scatteredlight polarization of the incident light (ei) is measured as Rei,and its amplitude observed in the es direction corresponds tothe inner product of es and Rei. Here, the E2g

1 and A1g Ramanmodes are considered to investigate the polarization depend-ence of the Raman intensity of WS2. The E2g

1 mode is doubly

degenerate and corresponds to the in-plane vibrations in thex−y directions, and the A1g mode is nondegenerate andcorresponds to out-of-plane vibrations of W and S atoms in theWS2 structure. The Raman tensors of these two modes are

= = − =Ra

a Rd

d Rb

bc

0 00 0

0 0 0,

0 00 00 0 0

,0 0

0 00 0

1E

2E A2g

12g1

1g

Ä

Ç

ÅÅÅÅÅÅÅÅÅÅÅÅÅÅ

É

Ö

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

Ä

Ç


É

Ö

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑ

Ä

Ç


É

Ö

ÑÑÑÑÑÑÑÑÑÑÑÑÑÑ(3)

where a, b, c, and d are major terms in the Raman tensor matrixand represent the physics of the interaction between crystallattice and light.29 As mentioned above, the E2g

1 mode is doublydegenerate, and therefore, it has two Raman tensors, as shown

in eq 3. R1E2g

1corresponds to the state that polarizability of the

lattice is in the x (or y) direction and polarization of the

incident light is in the y (or x) direction. R 2E2g

1corresponds to

the in-plane vibrations that the polarizability of the lattice andpolarization of the incident light are in the same direction. TheG peak of graphene paper has the same Raman tensors as theE2g1 peak of WS2 (or MoS2). In most published works, it is

assumed that a ≃ d. We perform our analysis based on thisassumption, and more discussion about it and its effects on ourcalculation will be provided in the next sections. The Raman

intensities of the E2g1 mode using two Raman tensors R1

E2g1and

R 2E2g

1are calculated as

β β

β β

β β

β β

∝ [| + |

+ | + | ]

∝ [| + |

+ | + | ]

I e R e e R e

e R e e R e

I e R e e R e

e R e e R e

( )cos ( )sin

( )cos ( )sin ,

( )cos ( )sin

( )cos ( )sin

E1

ss,t

1E

is

ss,t

1E

ip 2

sp,t

1E

is

sp,t

1E

ip 2

E2

ss,t

2E

is

ss,t

2E

ip 2

sp,t

2E

is

sp,t

2E

ip 2

2g1

2g1

2g1

2g1

2g1

2g1

2g1

2g1

2g1

2g1

(4)

where IE1

2g1 and IE

22g

1 are the intensities of the E2g1 peak, which

are calculated by R1E2g

1and R 2

E2g1, respectively. For example,

the term (ess, tR1

E2g1

eis) cos β is proportional to the Raman

intensity of the incident light, which is polarized in the sdirection and is calculated using the first Raman tensor of theE2g1 mode. By substituting eqs 1−3 into eq 4, we can calculate

IE1

2g1 and IE

22g

1 as

α β α β

α β α β

α β α β

α β α β

∝ [ + ] +[ − ]

∝ [ − ]+ [− − ]

I A B Da

A B

I A B

Da A B

(Ca) sin 2 cos cos 2 sin ( )

cos 2 cos sin 2 sin ,

(Ca) cos 2 cos sin 2 sin

( ) sin 2 cos cos 2 sin

E1 2 2 2

2

E2 2 2

2 2

2g1

2g1

(5)

Therefore, the Raman intensity of the E2g1 mode is expressed

as

β β= + ∝ [ + ][ + ]I I I a C D A B( ) ( cos ) ( sin )E E1

E2 2 2 2 2 2

2g1

2g1

2g1

(6)

Similarly, these calculations are conducted to find thepolarized-dependent Raman intensity of the A1g mode using itsRaman tensor, and the corresponding result is

β β∝ [ + ]I b AC BD( cos ) ( sin )A2 2 2

1g (7)



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To continue our investigation in polarized-dependentRaman intensities of the E2g

1 and A1g modes, we define twonew parameters as ψ = B/A and δ = D/C. ψ indicates theintensity ratio of the p-polarized photon to s-polarized photon,which are reflected by the beam splitter, and δ means theintensity ratio of the p-polarized light to the s-polarized lightthat are transmitted through the beam splitter. Figure 5 showsthe room-temperature WS2 Raman intensity variation withpolarization angle (β) for both Raman peaks. The dots indicatethe experimental data. Experimental data are fitted by a sine-squared function and represented by solid lines in Figure 5.The general form of this function is f(β) = Gsin2β + Kcos2β,

where G and K are fitting constants. By fitting the experimentaldata of the E2g

1 peak, we obtain ψ as ψ = =B A G K/ / . Inaddition, the ratio of G/K obtained by fitting the A1g datarepresents (BD/AC)2, and we define a third parameter as ϕ =BD/AC. Thus, ψ, ϕ, and δ for the supported or suspended areacould be found by fitting I against β of two peaks. The samecalculation is conducted for the temperature-dependentexperiment, and its results are shown in Figure 6. Figure 6a,c[or panels (b) and (d)] shows the experimental and fittingresults of the temperature-dependent experiment using thesupported (or suspended) area. Again, Figure 6 shows thevariation in Raman intensity in each temperature, which

Figure 5. Polarization-dependent Raman intensities of E2g1 and A1g modes of WS2 sample at room temperature for both supported and suspended

locations. Dots represent the experimental results and are fitted by a sine-squared function. The fitting results are shown by solid lines.

Figure 6. Temperature-dependent polarized Raman intensity against β for supported (a,c) and suspended (b,d) WS2 samples. Dots areexperimental data that are fitted by the sine-squared function (solid lines).



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confirms the resonant Raman effect at selected temperatures.The measured ψ, ϕ, and δ for each case are included in Table1. As mentioned earlier in the Introduction, there are several

polarized Raman configurations based on the position ofpolarizer(s), and these calculations are applicable for thoseconfigurations, too. For instance, in a system with a secondpolarizer that is placed before the spectrometer, it is stillnecessary to take the optical and structural effects intoconsideration.Results of the temperature-dependent experiment using the

WS2 sample on both areas are plotted, as shown in Figure 7, tostudy the effect of the sample’s temperature on ψ, ϕ, and δ. Forboth supported and suspended areas, ψ increases withincreasing temperature. Meanwhile, as temperature decreases,δ decreases, too. However, ϕ remains almost unchanged andfor all cases is around 0.75. Theoretically, all of these threeparameters correspond to the optical properties of our Ramansystem and should not be changed by the sample’s physics orits temperature. As we discussed earlier, both E2g

1 and 2LA(M)modes are present and are overlapping each other. Whentemperature increases from 300 to 450 K, the 2LA(M) peakbecomes weaker and it has less contribution in the combinedpeak that we use for our data analysis.27 Additionally, ψ onlydepends on A and B, which are measured by fitting thiscombined mode of E2g

1 and 2LA(M) modes. Therefore, asshown in Figure 7a,b by black lines, ψ experiences anincreasing trend by increased temperature. On the otherhand, as shown by eq 7, ϕ is measured by analyzing the A1gpeak, and since this peak is not overlapping other Ramanpeaks, we can fit it very precisely. Thus, ϕ is almost constantfor all of the temperatures and both supported and suspended

areas. Finally, since δ is calculated as δ = ϕ/ψ, it decreasesagainst the increased temperature, which is shown by blue linesin Figure 7a,b. These fitting results indicate that transmissionand reflectance of the beam splitter for the s- and p-polarizedlights are not exactly the same. Ideally for a 50:50 (R:T) beamsplitter, the transmission and reflection in either directionsshould be the same, while in the actual case, they are slightlydifferent. For instance, for a 1 mm thick 50:50 non-polarizingbeam splitter (BWS10R, ThorLabs) at 45° incidence, trans-mission values of s- and p-polarized lights are 41 and 56%,respectively. Additionally, reflection values of s- and p-polarized lights are 57 and 42%, respectively, for this beamsplitter. This means that reflection and transmission of s- andp-polarized lights are different, even for a 50:50 non-polarizingbeam splitters. As the reflection-to-transmission ratio (R:T)deviates from 50:50, the difference between the transmissivityand reflectivity in each direction becomes even more obvious.

3.3. Polarized Raman of MoS2 and Graphene Paper.In this section, MoS2 and graphene paper are used to verify theanalysis that was conducted in the last section and providemore explanations. For these two materials, only the room-temperature polarized Raman experiment is conducted. Usingour Raman system, both E2g

1 and A1g peaks of MoS2 as well asthe G peak of graphene paper are observed and used toperform the analysis.Results of the MoS2 experiment are plotted in Figure 8a−c.

Figure 8a shows the Raman spectrum of MoS2 under differentpolarization angles. As β increases from 0 to 180°, the Ramanintensity of the A1g mode first decreases until β = 90°, and thenit increases again. However, the Raman intensity of the E2g

1

mode changes differently, and it reaches the maximum at β =90°. This behavior of two peaks is more obvious in the polarplot, as shown in Figure 8b. The polar plot of the Ramanintensities of two peaks indicates the 90° phase differencebetween the E2g

1 and A1g modes. Figure 8c shows the Ramanintensity of each MoS2 Raman peak against β as well as thefitting lines using the sine-squared function. ψ, ϕ, and δ of theMoS2 sample are measured and indicated in Table 1.Figure 8d shows several representative Raman spectra of

graphene paper at different β and room temperature. The polarplot of the Raman intensity of the G peak and fitted data usingthe sine-squared function are shown in Figure 8e,f,respectively. The result of this measurement is included inTable 1. Note that, by using this sample, it is only possible tomeasure ψ using the G peak.As indicated by Table 1, ψ values of WS2, MoS2, and

graphene paper are in very good agreement with each otherand are around 0.85. Any discrepancy between the ψ measuredusing WS2 sample and two other samples could be caused by

Table 1. Measured ψ, ϕ, and δ for WS2 at DifferentTemperatures and MoS2 and Graphene Paper Samples atRoom Temperature

material T (K) ψ ϕ δ

WS2 (supported) RT 0.874 0.762 0.872270 0.847 0.747 0.882317 0.843 0.707 0.838417 0.882 0.742 0.841445 0.905 0.737 0.814

WS2 (suspended) RT 0.876 0.769 0.879300 0.868 0.758 0.873337 0.876 0.755 0.861420 0.912 0.748 0.819

MoS2 (supported) RT 0.812 0.741 0.912graphene paper RT 0.885

Figure 7.Measured ψ (left vertical axis), ϕ (middle vertical axis), and δ (right vertical axis) for (a) supported and (b) suspended WS2 samples. Theincreasing (decreasing) trend in ψ (δ) by increased temperature is caused by the effects of the 2LA(M) mode Raman intensity change againstsample temperature.



23242


the quality of data fitting. As mentioned earlier, the 2LA(M)and E2g

1 peaks of WS2 overlap at our working temperature, andas a result, it causes some uncertainty in data analysis. Inaddition, transmission and reflection of a specific beam splittervary with the light wavelength. In this work, since thewavelength of incident laser is always 532 nm, there will be nodifference between the reflectivity of the beam splitter.Meanwhile, for the scattered light, which corresponds to δ,transmission of the beam splitter could be different fordifferent Raman modes of WS2, MoS2, and graphene. This isanother reason for discrepancy between δ values in Table 1.Additionally, there is an around 80° phase difference betweenthe polar plot of the E2g

1 mode of MoS2 and polar plot of the Gpeak. This difference could be caused by the assumption thatelements of Raman tensors of the E2g

1 mode are equal (eq 3).Neglecting this assumption will result in a phase shift inside thesine-squared function. To evaluate this claim, the Ramanintensity of the E2g

1 mode is calculated by considering itsRaman tensors with different elements as

α α β

α α β

∝ [ + + − ]

+ [ − + − − ]

I C Ac Bd C Ad Bc

D Ad Bc C Ac Bd

( cos 2 )( ) ( sin 2 )( ) cos

( cos 2 )( ) ( sin 2 )( ) sinE

2 2

2 22g1

(8)

As shown in eq 8, the Raman intensity of the E2g1 mode is not

only a function of β but also α. Regarding the E2g1 peak of the

WS2 sample, its phase shift is in between the G peak and E2g1

peak of MoS2, and as temperature goes higher, it becomescloser to MoS2. Theoretically, its phase shift should be similarto the MoS2 sample. Again, this difference could be caused bythe effect of the 2LA(M) mode on the data fitting. However,the Raman intensity of the 2LA(M) mode is weaker at highertemperatures,27 and the polar plot of the E2g

1 mode of WS2 isexpected to be similar to the MoS2 polar plot at very hightemperatures.So far, we have discussed about the effects of sample

preparation, working temperature, and beam splitter onpolarized Raman spectroscopy. Note that aforementionedoptical effects depend on the optical properties of theconfiguration and will affect the polarized Raman intensityregardless of the material. Therefore, these effects need to beconsidered for other materials, such as silicon, carbon

Figure 8. Room-temperature polarized Raman experiment using MoS2 and graphene paper. Seven representative Raman spectra of (a) MoS2 and(d) graphene paper at different polarization angles are presented. Polar plots of Raman intensities for (b) E2g

1 and A1g peaks of MoS2 and (e) G peakof graphene paper. There is an around 80° phase difference between the polar plots of the E2g

1 peak and A1g or G mode. Fitting results of thisexperiment using (c) MoS2 and (f) graphene paper. The fitting function is similar to the sine-squared function used to fit the WS2 experimentresults.



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nanotubes, and black phosphorus. Especially in applicationslike identifying the crystalline orientation of black phosphorus,it is critical to consider these effects for more accurate analysis.For silicon, since it is not perfectly isotropic and could havedifferent behaviors in both s- and p-polarized directions, theseoptical effects could affect the final polarized Raman intensity.Also, regarding carbon nanotubes, they have different polar-ization behaviors in the axial and radial directions, so theeffects discussed in this paper should be considered in detail.Meanwhile, there is another point that needs to be taken intoconsideration, and that is the grating sensitivity for the twopolarization directions. As shown in Figure 1a2, gratingdiffracts light into several beams in different directions.Raman intensities in both s- and p-polarized directions ideallyshould be the same for a specific grating configuration, butpractically, they are not. However, grating reflectivity dependson polarization, detecting wavelength, groove density, andgroove profile. In this work, the last three factors have a lesseffect on accuracy of this measurement, while the polarizationeffect is more important.

4. CONCLUSIONSIn this work, few-layered WS2 and MoS2 as well as bulkgraphene paper were used for studying their intensityresponses to polarized Raman excitation laser. It was reportedin previous works that Raman intensities of the E2g

1 and Gmodes are independent of the polarization angle and do notchange with β, while a strong dependency on β was discoveredin this work for all three materials. The E2g

1 and A1g Ramanmodes of nanometer-thick WS2 and MoS2 samples as well asthe G Raman peak of bulk graphene were used to investigatethe polarization dependency of the Raman intensity for eachmode. The incident laser was polarized using a polarizer beforeirradiating the sample. Using the WS2 sample, we investigatedthe effect of temperature and sample structure on the polarizedRaman signal. The polarized Raman experiment wasconducted on both supported and suspended areas ofexfoliated WS2. These experimental data were verified andfitted by the classical theory of Raman scattering, whichconsiders the polarization direction of the incident laser,different vibrational modes regarding each Raman mode, androtation of the beam splitter about the z axis. It was conclusivethat the Raman intensity variation with incident laserpolarization is a function of the polarization angle (β) andincludes information about optical components of the Ramansystem, especially the beam splitter.

■ AUTHOR INFORMATIONCorresponding Authors*E-mail: [email protected]. Tel: 011-86-13647662074 (Q.Z.).*E-mail: [email protected]. Tel: 001-515-294-8023 (X.W.).ORCIDXinwei Wang: 0000-0002-9373-3750Author Contributions∥H.Z. and R.W. contributed equally to this work.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSFinancial support of this work by the College of Engineering ofIowa State University is gratefully acknowledged.

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